Question

How do you change bounds when you integrate by substitution method?

Answer 1

Use the substitution you made and arithmetic.

For `int_1^4 (5-3x)^4 dx`

You'll substitute `u=5-3x` which makes `du = -3dx` and `dx= - 1/3 du`

It also makes the lower limit of integration: `5-3(1) = 2` (When `x=1`, `u=2`

And the upper limit of integration becomes `5-3(4)= - 7`.

With these substitutions, we now need to find:

`-1/3 int_2^(-7) u^4 du`